Physics 1425: General Physics I

Spring 2010

Michael FowlerRoom 307, Physics

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Today’s Topics

• Course arrangements, syllabus outline.• Nature of science: observation and

measurement.• Accuracy, significant figures.• Units, mass of water, estimation.• Unit conversions, useful approximations.

Basic OutlineThe course has three main parts, each about a month, each followed by a midterm-like exam.

1. Dynamics, Newton’s Laws, gravitation.2. Work, energy and momentum conservation,

torque and rotational dynamics.3. Fluids, simple harmonic motion, heat and

thermodynamics.

Part I: Dynamics

1. Preliminaries: measurement, estimation.2. One-dimensional motion: velocity and acceleration.3. Projectile motion, vectors.4. Newton’s Laws of Motion.5. Vector force diagrams. Friction.6. Dynamics of circular motion.7. Gravitation: Kepler’s Laws, Newton’s Law.

Nature of Science

www.mlahanas.de/Greeks/AristotleBiol.htm

Observation: here’s Aristotle observing and noting.

Theorizing: finding general laws.

Checking: observe more and do experiments to check the theory!

Aristotle’s Law of Motion:

Things move if pushed. Otherwise not. Wrong!

Better Observation: Galileo

• Invented the telescope, found the Moon not a perfect sphere, as believed.

• Studied motion: imagined a rolling ball without friction: would continue indefinitely, without being pushed!

Measurement and UncertaintyGalileo, the first real physicist, also experimentally measured acceleration: the rate of increase of speed, of a falling object. He found the acceleration to be constant, at his level of accuracy.

How do we quantify level of accuracy?Need explicit statement of expected error:

Example: timing a 100 yard run with a stopwatch,10.5± 0.1 seconds: Most likely 10.4 to 10.6 secs.

Significant Figures

Number of reliably known digits: not counting initial zeroes.Examples: 62.0 three sig figs0.0033 two sig figs

It’s a measure of claimed accuracy.

Clicker Question!

0.0120 has how many significant figures?

A. 2B. 3C. 4D. 5

Important

The accuracy of output of a calculation cannot exceed the accuracy of any of the input!

Calculators don’t know this—you need to:1.000/7.0 = 0.14 (correct)NOT 0.142857142857…

DON’T write down meaningless digits!(that 7.0 might more precisely be 7.03 or 6.96)

SI Units

Time: unit 1 second: defined as time for a certain excited atom (cesium) to make a specified number of oscillations.

Length: unit 1 meter: defined as distance light travels in a specified fraction of a second.

(The actual number of cesium atom oscillations (about 9 billion) is in the book, as is the precise distance—laser jocks know the speed of light is about one foot per nanosecond, but that’s non-SI.)

SI Unit: Mass• The unit of mass is the

kilogram, defined as the mass of a chunk of platinum in Paris, shown here.

• From: http://en.wikipedia.org/wiki/File:CGKilogram.jpg

• In2011, a committee will recommend a more fundamental atomic definition.

Useful Fact: the Mass of Water

One liter of water has a mass of one kilogram.

One cubic meter is 1,000 liters.

One cubic meter of water has a mass of 1,000 kg, one metric ton, about 2,200 lbs.

Clicker Question: what is your volume in cubic meters, approximately?

A. 0.3B. 0.2C. 0.1D. 0.07E. 0.05

Powers of Tenthe video

Review Scientific Notation:1,234,000 = 1.234 x 106

0.0000123 = 1.23 x 10-5

Review factors of powers of 10 prefixes:Most common are: (up) kilo, mega, giga, tera, … (down) milli, micro, nano, pico, …Each up or down from the next by a factor of 1,000

Converting Units

We’ll work in SI units: but in the US other units are more common.Exact conversion factors are in the book and elsewhere

BUT it’s useful to memorize approximateequivalents for making rough estimates!

Examples ….

Useful Approximations

1 ft ≈ 30 cm 1 meter ≈ 1.1 yards5 miles ≈ 8 kilometers50 mph ≈ 80 kph ≈ 22 m/sec

1 kg ≈ 2.2 lbs (technically, kg is mass, lb is weight—so this isn’t true on the Moon!)

1 gallon ≈ 4 liters

Rough Estimation

http://en.wikipedia.org/wiki/File:Dubail21.jpg

• The new Dubai skyscraper is just over 800 meters high.

• The view from the top extends to about 100 km.

• What is the radius of the Earth?

D is the top of the Dubai tower, F is the far horizon, C is the center of the Earth. DF is perpendicular to FC. If the radius of the Earth is R, and the tower has height h, and the furthest visible distance is d, then R2 + d2 = (R + h)2.

D

F

C

So d2 = 2Rh + h2, but h is much smaller than R, so the h2 is negligible, we can say d2 = 2Rh.

If a replica of the Dubai tower were erected on the Moon, how far away would you be able to see the Moon’s surface from the top?

(The Moon’s diameter = 0.25 Earth diameters, approximately.)

A. 400 kmB. 200 kmC. 100 kmD. 50 kmE. 25 km